You still need to record the timezone somewhere and you might as well just stick to ISO8601/RFC3339 format then.
If you get timestamp data from a system outside of your control though you always have to make sure you know what it means. At least half the time it seems like a date without a timezone isn't UTC, but in whatever the originating timezone was but the developers didn't include a timezone offset in the data...Timezones....the bane of my existence.